Global sensitivity analysis and robustness in linear programming using different norms

Sensitivity analysis in linear programming is a standard technique for measuring the effects of variations in one coefficient on the optimal value and optimal solution. However, one-coefficient variations are too simple to reflect the complexity of real-life situations. That is why we propose a more general approach and consider variations of possibly all input data. The goal is to determine the maximum variations of the data in a given norm such that the computed optimal basis remains optimal. We present general results valid for an arbitrary norm, and then we focus particularly on the spectral norm and the maximum norm. Further, we analyse computational complexity of the problem, and for the computationally hard cases we derive efficiently computable lower and upper bounds. Besides the basic case, in which we allow variations of all input coefficients, we also consider variations of certain submatrices or along a certain pattern. Eventually, we present results of numerical experiments, where we analysed and compared computation time and accuracy of the proposed approximations on a collection of dataset.